The extraction of the topology of shapes is a basic building block for modeling physical processes. Many natural topologies (neural anatomy and the botanical structure of plants) can be described by a binary branching tree structure (Verwer R W H, J Van Pelt, 1983, “A new method for the topological Analysis of Neuronal Tree Structures.” J Neurosci Meth, 8, 335–351). Many organic processes such as the electrophysiological processes of the neuron are influenced by their morphological properties (Ascoli A. Giorgio, Progress and Perspectives in Computational Neuroanatomy, Anatomical Record (The New Anatomist section), 257(6):195–207 (1999)).
The current state of the art models these objects as a connected series of elements. The geometry of the object is described by listing the coordinates of the elements along with a reference to the elements parent or child. This referencing system allows the topology of the object to be maintained. A drawback of this method is that adjacent elements in the object may not be adjacent in the file structure. This means a referencing system is required to navigate the elements in a manner dictated by the object being modeled.